CANTON  Count on Cantor
One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.
1/1 1/2 1/3 1/4 1/5 ... 2/1 2/2 2/3 2/4 3/1 3/2 3/3 4/1 4/2 5/1
In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.
Input
The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.
Then, it contains a single number per line.
Output
You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.
Example
Input: 3 3 14 7 Output: TERM 3 IS 2/1 TERM 14 IS 2/4 TERM 7 IS 1/4
hide comments
yead_025:
20171115 15:04:53
O(1) 

sanyam19:
20171023 21:18:02
AC in one go.....one should first observe d pattern..if want to make a formula,try to observe num nd den... Last edit: 20171023 21:18:32 

sohailwiiierd:
20171021 21:00:44
the corners.......... 

hitesh87:
20170927 20:22:20
Very nice problem. AC in one go. 

bhuvi9:
20170817 11:51:59
took 5 hours to solve it. 

imranjeetsingh:
20170712 16:08:17
took some time but AC in one go.


manish_nit97:
20170703 21:16:37
After thinking for the pattern at a continuous stretch of 1.5 hours finally got the logic.


dr_br34k:
20170627 14:58:37
Think of O(1) solution every ith new slant line is made of i elements.


anilkumar1998:
20170609 19:44:47
Try to think of O(1) solution. 

codervrinda:
20170529 07:09:27
nice problem:) !

Added by:  ThanhVy Hua 
Date:  20050227 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  ACM South Eastern European Region 2004 